Existence of one weak solution for p(x)-biharmonic equations involving a concave-convex nonlinearity

Abstract

In the present paper, using variational approach and thetheory of the variable exponent Lebesgue spaces, the existence of nontrivialweak solutions to a fourth order elliptic equation involving a$p(x)$-biharmonic operatorand a concave-convex nonlinearity the Navier boundaryconditions is obtained.